Elsevier eBooks

Methods of Investigating Non-Equilibrium States of Quantum Systems

Alexander I. Akhiezer, S. V. Peletminskiǐ

Published Jan 1, 1981• 0 citations

DOI: 10.1016/b978-0-08-025040-3.50009-2

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The quick progress in quantum entanglement research allows us not one to study quantum systems down to N-bodies but also to take a new look at these systems in different branches of physics; particularly the statistical thermodynamics where the application of the thermo-field dynamics (TFD) method to the investigation of entanglement is fruitful. Because the traditional methods based on the identification of a specific parameter show their limit. The process using (TFD) facilitates the understanding of entanglement because it focuses directly on the eigenstate of the system and it is useful in the equilibrium and the non-equilibrium states also. In this context, the (TFD) method is used in this paper to analyze entanglement of an electron interacting with a two-mode electromagnetic field assimilated to an electron with two harmonic oscillators. Entanglement entropies are derived between concerned, not concerned harmonic oscillator and electron compute when the system is in a thermodynamic equilibrium and non-equilibrium state. For the equilibrium case, an increase in the number of particles per unit volume increases the quantum entanglement consequently entanglement appears more important for the couple oscillator-electron than the one electron, this trend is reversed for the non-equilibrium case. By respecting the entanglement parameters, such results allow us to know the relative equilibrium state of the overall system.

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In this thesis focus is laid on fluctuation theorems in autonomous modular quantum systems. Moreover, non-equilibrium cyclic processes using a quantum system as working agent are investigated. The first part is concerned with possible pitfalls in adopting idealized model systems from quasistatic thermodynamics for processes driving the system far away from equilibrium. Investigations of a one-dimensional quantum analogue of a gas confined in a cylinder show that the idealization of the cylinder as being absolutely impenetrable leads to questionable results when the gas is in a highly non-equilibrium state during an enforced process. Only when the quasistatic case is recovered, this idealization, well proven in equilibrium thermodynamics, regains its validity. For the investigations concerning fluctuation theorems this thesis focuses on the Jarzynski relation which relates the work performed during a non-equilibrium process with the free energy difference of two equilibrium states. In order to formulate the Jarzynski relation for a specific local part of a closed modular quantum system, the energy transfer between different subparts has to be divided into work and heat, respectively. This separation is performed using LEMBAS, a method to distinguish between heat and work for quantum systems in arbitrary states. In the second part functional environments for a system of interest are identified by using LEMBAS. These functional environments are classified as work or heat sources, respectively. Using these work and heat sources in the third part, different estimation methods for the local effective free energy for the system of interest are studied. This way it is shown that it is possible to generalize the Jarzynski relation to local effective dynamics, giving good estimates for the free energy difference if the correct estimation method is used. In this context, LEMBAS provides a feasible separation of heat and work. The last part of this thesis is concerned with a quantum generalization of the classical Otto cycle. The working agent is to be taken as a quantum system whereas the heat baths are assumed to be classical. For this setting the efficiency of cyclic processes is shown to be limited by the corresponding classical efficiency.

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Statistical physics provides the concepts and methods to explain the phase behavior of interacting many-body systems. Investigations of Lee-Yang zeros - complex singularities of the free energy in systems of finite size - have led to a unified understanding of equilibrium phase transitions. The ideas of Lee and Yang, however, are not restricted to equilibrium phenomena. Recently, Lee-Yang zeros have been used to characterize non-equilibrium processes such as dynamical phase transitions in quantum systems after a quench or dynamic order-disorder transitions in glasses. Here, we experimentally realize a scheme for observing Lee-Yang zeros in such non-equilibrium settings. We extract the dynamical Lee-Yang zeros of a stochastic process involving Andreev tunneling between a normal-state island and two superconducting leads from measurements of the dynamical activity along a trajectory. From short-time observations of the Lee-Yang zeros, we predict the largedeviation statistics of the activity which is typically difficult to measure. Our method paves the way for further experiments on the statistical mechanics of many-body systems out of equilibrium.

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